Traditional ligand-field theory has to be improved by taking into account both "pure electronic" contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R1, R2, R 3 , R 2 , and R 1 lines, U band, ground-state zero-field-splitting (GSZFS), and ground-state g factors of ruby and/or GSGG: Cr 3+ as well as thermal shifts of GSZFS, R1 line and R2 line of ruby have been calculated. The results are in very good agreement with the experimental data. Moreover, it is found that the value of cubic-field parameter given by traditional ligand-field theory is inappropriately large. For thermal shifts of GSZFS, R1 line and R2 line of ruby, several conclusions have also been obtained.

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The d3 ions in trigonal crystal fields are considered. On the basis of the expansion of the electron wavefunctions under pressure. the expressions for the parameters Dg. E , C. K. K' and( as functions of the linear compression ratio x are derived, and the complete d3 energy matrix in trigonal field is constructed. Wtth the P-.y dependence, by diagonalizafion of this matrix to fit only the experimental data of the red shifts of Nby RI line under quasihydrostatic pressure. the valves of three parameters for the pressure shin ($, DI and t ) are determined. Then. the values of Dq, B, C. K. K' and at various pressures are evaluated, and the pressure shins of the entire energy s p e c " of Nby are theoretidy calculated uniformly by diago&tion of the complete d3 matrix. The contributions of changes of Dq, B, C, K, K' and < to the RI and Rz red shifts and the pressure-induced change in lhe RI-R~ splitting are obtained. The wlculated results of Ihe pressure shifts are in good agreement with all the experimental data of the R-. RIand B-line groups and U and Y bands. A discussion is given and conclusions drawn.

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